It has nothing to do with ownership. In FP, a function can only operate on data of a particular type. In OOP, a particular type (or class) gathers all the applicable functions (or methods) under one roof. Same difference.
Maybe my point is better articulated by saying [to me,] functional programming is more data oriented than OOP.
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OO is different because you have things like private variables. Meaning that only methods of an object's class can access the variable. So you now have a special group of functions that can access the variable. FP is not like that.